Finite Group Databasebeta

← #30605529

Subgroups — #30605529

Order 15616.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462188C212yesmaximal, complemented
2#21460821C214yesmaximal, complemented
3#21456193C211yesmaximal, characteristic
4#16840685—22no—
5#16840658—22no—
6#16840654C2214yescomplemented
7#16840319C411yescharacteristic
8#16840126C412yes—
9#16840126C2212yes—
10#16840108—22no—
11#16839767—22no—
12C4×#11758194C2211yescharacteristic
13C2×#127×C61C411yescharacteristic
14#14519851—24no—
15C2×#11758194D412yes—
16#14519777—21no—
17#14519769C2×C412yes—
18#14519756—41no—
19C4×Dic122—41no—
20#14519736—21no—
21#14519698—24no—
22#14519698—24no—
23#14519688C2×C411yescharacteristic
24#14519688C2311yescharacteristic
25C4×#92418D412yes—
26C22×D4×C61—21no—
27C22×D4×C61—41no—
28#127×C61—21no—
29#127×C61—41no—
30#127×C61C2×C412yes—
31C2×C42×C61C2×C411yescharacteristic
32C24×C61—41no—
33C2×D4×C61—22no—
34C2×D4×C61—44no—
35C2×D4×C61—42no—
36C2×D4×C61—42no—
37C2×D4×C61—41no—
38C2×D4×C61—84no—
39C22×C4×C61—21no—
40C22×C4×C61C22⋊C411yescharacteristic
41C2×Dic122—41no—
42C42×C61—21no—
43C42×C61C22⋊C411yescharacteristic
44C42×C61C22×C411yescharacteristic
45C22⋊Dic61—41no—
46C4⋊Dic61—22no—
47C4⋊Dic61—41no—
48#11758196—42no—
49C4×Dic61—41no—
50#11758194—42no—
51C2×#92418C22⋊C412yes—
52C2×#92418C2×D412yes—
53#11758187—44no—
54C23×C61—42no—
55C23×C61—82no—
56C23×C61—84no—
57C23×C61#10011yescharacteristic
58D4×C61—44no—
59D4×C61—82no—
60D4×C61—84no—
61D4×C61—84no—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—42no—
66C2×C4×C61#10011yescharacteristic
67C2×C4×C61C2×C22⋊C411yescharacteristic
68C2×Dic61—42no—
69Dic122—82no—
70#92418—22no—
71#92418—22no—
72#11915—611nomaximal, Sylow
73C22×C61—21no—
74C22×C61—41no—
75C22×C61—84no—
76C22×C61—82no—
77C22×C61—164no—
78C22×C61C2×#10011yescharacteristic
79C4×C61—22no—
80C4×C61—21no—
81C4×C61—41no—
82C4×C61#42112yes—
83Dic61—82no—
84#3138—611no—
85#2165—612no—
86#1355—614no—
87C2×C61—21no—
88C2×C61—41no—
89C2×C61—162no—
90C2×C61#153311yescharacteristic
91#533—611no—
92C2×#127#692311yescharacteristic
93#490—612no—
94#490—612no—
95#486—1222no—
96#418—1222no—
97C4×M16—611no—
98#364—1222no—
99#349—1222no—
100#347—614no—
101C61#1191511yescharacteristic, complemented, Sylow
102C22×D4—21no—
103C22×D4—41no—
104C2×M16—612no—
105C4⋊Q8—1221no—
106#127—21no—
107#127—41no—
108#127C2×#692312yes—
109#125—612no—
110C22⋊Q8—2441no—
111C4×Q8—2441no—
112#117—1221no—
113C2×C42C2×#692311yescharacteristic
114M32—1224no—
115#102—1224no—
116#102—1224no—
117#97—611no—
118#97—611no—
119C4×C8—612no—
120C24—41no—
121C2×Q8—2441no—
122C2×D4—22no—
123C2×D4—44no—
124C2×D4—42no—
125C2×D4—42no—
126C2×D4—41no—
127C2×D4—84no—
128C22×C4—21no—
129C22×C4C22⋊#692311yescharacteristic
130M16—2442no—
131C2×C8—612no—
132C2×C8—612no—
133C4⋊C4—1222no—
134C4⋊C4—2442no—
135C4⋊C4—2441no—
136C22⋊C4—2441no—
137C42—21no—
138C42—2441no—
139C42C22⋊#692311yescharacteristic
140C42C22×#692311yescharacteristic
141C16—2444no—
142C23—42no—
143C23—82no—
144C23—84no—
145C23#1451983711yescharacteristic
146Q8—4882no—
147D4—44no—
148D4—82no—
149D4—84no—
150D4—84no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—42no—
155C2×C4—2442no—
156C2×C4#1451983711yescharacteristic
157C2×C4C2×C22⋊#692311yescharacteristic
158C8—1222no—
159C8—1222no—
160C22—21no—
161C22—41no—
162C22—84no—
163C22—82no—
164C22—164no—
165C22C2×#1451983711yescharacteristic
166C4—22no—
167C4—21no—
168C4—41no—
169C4—4882no—
170C4#1684076012yes—
171C2—21no—
172C2—41no—
173C2—162no—
174C2#2146129811yescharacteristic
subgroupG/H
centerC2#21461298
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
Fitting, prime radicalC2×#127×C61C4
socleC2×C61#1533
cosocle#14519688C23
hypercenterC2×#127#6923
hypocenterC61#11915
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#127

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21462188C2semidirect
2. #21460821C2semidirect
6. #16840654C22semidirect
101. C61#11915semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214621882
#214608212
#214561932
#1191561